The Gaza Youth Breaks Out group said the man, identified only as Abu Yazan, had gone missing shortly after being called in for two separate interrogations by Hamas forces after his return from a speaking tour in France.
They declined to give his name, citing the security of his friends and family.
The 25-year-old was a founding member of Gaza Youth Breaks Out, which grabbed attention with its December 2010 manifesto condemning Hamas, Fateh and Israel, and calling for freedom, "a normal life", and peace.
Another member of the group, who identified himself only as Abu Ghassan, said Abu Yazan had been missing since he went to try to retrieve his laptop and mobile phone from the headquarters of Gaza internal security services.
"There was a threat that he would be arrested and he had to turn over his laptop and mobile phone to the internal security before he went to France," Abu Ghassan said.
"He went to get his laptop and mobile phone back two days ago and since then he hasn't been seen or heard from.
"They knew him very well and they knew that he was such an active guy and I fear that when he came back from France, it was an easy excuse for them to say he was involved in foreign interference or something," he added.
Abu Yazan was also an active member of the March 15 movement, which staged massive protests calling for Gaza's Hamas rulers to reconcile with their long-time political rivals, Fatah.
He also helped to organise weekly demonstrations against the so-called buffer zone, a strip of land which runs the entire length of the Gaza border which has been deemed a no-go zone by the Israeli army, Abu Ghassan said.
"This is probably the third time that he's been arrested. He was beaten up for a day or two and then released. We know nothing of his whereabouts," he said.
The government had no immediate comment on the reported arrest, declining to confirm or deny it.
In March, US-based group Human Rights Watch accused Hamas of suppressing peaceful protests in Gaza and called on the group to investigate claims that its security officers tortured an activist involved with the March 15 movement.
"The Hamas government has shown time and again that it cares little about the rights of Palestinians who peacefully challenge its policies," the group said in a statement at the time.
"Hamas says it's fighting for liberation from occupation but is repressing people living under its control."
Maan News Agency